Flat Galactic Rotation Curves Interpreted as Evidence for the Mach's Principle

Abstract

We explore the possibility of a Machian interpretation for the phenomena associated with asymptotically flat rotation curves in disk galaxies, providing an alternative to both the Lambda-Cold Dark Matter ($\Lambda$CDM) paradigm and MOdified Newtonian Dynamics (MOND). We argue that the MOND acceleration scale $a_0$ is likely not a new fundamental constant, but rather a manifestation of the cosmological scales of the observable Universe ($a_0 \sim c^2/R_u \sim c^4/GM_u \sim c/t_u$). We rewrite the Baryonic Tully-Fisher Relation (BTFR) in a cosmological format, $\frac{M_{\rm bar}}{M_{u}} = \left( \frac{V}{c} \right)^4$, suggesting that the transition to the non-Newtonian regime occurs when local accelerations become small enough to feel the global cosmic boundary, and showing that any Machian interpretation must fulfill a relation of this form. Furthermore, this framework naturally predicts a cosmological evolution of the BTFR normalization as the mass in the observable Universe evolves. We test these predictions against recent high-redshift observations ($z \sim 2$ and $z \sim 5$), finding that the data favor a flat, baryon-only, $\Lambda$-dominated quasi-de Sitter universe ($\Omega_m \approx 0.05$, $\Omega_\Lambda \approx 0.95$) over standard MOND or $\Lambda$CDM parameters. These results suggest that flat galactic rotation curves may be interpreted as compelling evidence in favor of Mach's Principle, in at least some of its versions.